Finance Minister Harris Georgiades described the situation as "extremely difficult," before the parliament met at 2 p.m. London time on Tuesday to ratify the terms of the aid package.

Without a bailout, Cyprus would face "incomparably tougher difficulties" and a fiscal "nightmare," Georgiades told lawmakers.

No single party has a majority in the 56-member parliament and the government was counting on the support of its three party center-right coalition, which has 30 seats.

The Communist AKEL party, socialist Edek party and the Green Party previously said they would reject the bill.

Bailout Will Create Loans for 23 Years: Green Party

Efi Xanthou, International press relations for the Green Party in Cyprus, tells CNBC that she continues to oppose the euro zone bailout as it will destroy Cyprus's financial sector which made up 40 percent of GDP.

Efi Xanthou, the head of international press relations of the Green Party in Cyprus, told CNBC that bailout conditions would inflict more "chaos" on the island.

"We continue to oppose the bailout—or bail-in—we believe the memorandum [of understanding] requirements are not going to help us exit this economic depression. We believe it will create even more chaos and economic dependence on foreign loans," she told CNBC Europe's "Squawk Box."

In March, the Cypriot parliament agreed to a 10 billion euro deal with international lenders that involved the "bailing-in" of banking deposits with more than 100,000 euros. The deal also stipulated that Cyprus should make public sector spending cuts and consider selling public assets and its gold reserves.

It was followed by a two-week shutdown of banks as the second-largest Cypriot bank, the Laiki (Popular) Bank, was wound down and insured deposits of under 100,000 euros were transferred to the Bank of Cyprus.

"Basically we're seeing the destruction of our financial and economic center. This sector accounted for 40 percent of the country's GDP and businesses are shutting down because there's not enough liquidity in the market and they can't get credit from their banks," Xanthou added.

She called for further negotiations to get a better "solution" and "compromise" to the crisis.

Thanos Papasavvas, fixed income and currencies strategist at Investec Asset Management, told CNBC that markets had been correct in remaining calm over the Cypriot bailout and Italian political deadlock.

"The markets have correctly isolated these events with the understanding that politicians and policy makers will do whatever it takes to keep the euro zone intact," he told CNBC on Tuesday.

"Even if, for an unfortunate reason, Cyprus were to vote to leave the euro zone it would not create contagion in the euro zone—it would be disastrous for Cyprus—but it would not create a problem for the euro zone," he said.